The H i-rich ultra-diffuse galaxies follow the extended Schmidt law

Abstract

ABSTRACT The ${\rm H\, {\small I}}$-rich ultra-diffuse galaxies (HUDGs) offer a unique case for studies of star formation laws as they host low star formation efficiency and low-metallicity environments where gas is predominantly atomic. We collect a sample of six HUDGs in the field and investigate their location in the extended Schmidt law ($\Sigma _{\text{SFR }} \propto \left(\Sigma _{\text{star}}^{0.5} \Sigma _{\text{gas}}\right)^{1.09}$). They are consistent with this relationship well (with deviations of only 1.1σ). Furthermore, we find that HUDGs follow the tight correlation between the hydrostatic pressure in the galaxy mid-plane and the quantity on the x-axis ($\rm log(\Sigma _{star}^{0.5}\Sigma _{gas})$) of the extended Schmidt law. This result indicates that these HUDGs can be self-regulated systems that reach the dynamical and thermal equilibrium. In this framework, the stellar gravity compresses the disc vertically and counteracts the gas pressure in the galaxy mid-plane to regulate the star formation as suggested by some theoretical models.